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NMR Studies in Hexaborides Diplomarbeit in experimenteller Festkörperphysik.

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ISBN: 3817116829 ISBN: 3817116829 ISBN: 3817116829 ISBN: 3817116829

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Next: Summary Up: Results Previous: The Spin-Spin Relaxation Rate

Discussion

From the very low charge carrier density at the Fermi level in SrB₆ and CaB₆ one expects no or only a very small Knight shift in these materials. This expectation agrees very good with the measurements.

The central line of both samples is inhomogeneously broadend. But the width of 2.5kHz (35 p.p.m.) is that narrow, that we can not separate the effects which may have caused this broadening. The very narrow line can be a certain evidence that the sample is of a high quality.

Summarized we did not see any unexpected effects in the spectra.

But in the spin-lattice relaxation rate we found a very exciting behaviour which is up to now not understood. It is not compatible with what we know from paramagnetic metals or semiconductors. Around T_</I>B the relaxation rate 1/T₁ is surpisingly large. Attempts to associate the relaxation rate with excitations related to the weak ferromagnetism failed in the temperature independent or even slightly decreasing behaviour of 1/T₁ above T_</I>B.

In the scope of this work we want to accept that the relaxation rates of CaB₆ and SrB₆ and their coincidence at the moment only add another puzzle to the features of these compounds. We are not going to make any speculations about the origin of this effect. We only want to give some evidence that we are investigating an intrinsic effect of the complex (electronic) structure of CaB₆ and SrB₆.

The main objection we had to fight was that we were not measuring an intrinsic property of these Hexaborides but instead seeing an effect of paramagnetic impurities. As already mentioned in section there has been done some work about paramagnetic impurities in metals [#!mchenry!#,#!giovannini!#]. According to them the spin-lattice relaxation rate of a metal with paramagnetic impurities behaves in the case of longitudinal dipolar coupling like:

$\begin{displaymath}T_1^{-1} \propto \frac{\partial B_S(\alpha)}{\partial \alpha}, \end{displaymath}$ (4.1)

with

$\begin{displaymath}\alpha = \frac{g \mu_\mathrm{B}SH}{k_\mathrm{B} T}, \end{displaymath}$ (4.2)

$B_S(\alpha)$ the Brillouin function and S the spin.
In the case of transverse dipolar coupling they found:

$\begin{displaymath}T_1^{-1} \propto \frac{B_S(\alpha)}{\alpha}. \end{displaymath}$ (4.3)

This model applies in the case where we have single paramagnetic impurities, which is equivalent to the restriction that the coupling of the impurity spins with the external field is much larger than the coupling among themselves. If we would have paramagnetic impurities in our sample this would certainly apply to them.
But as can be seen from equation () or () in the case of paramagnetic impurities the curves of 1/T₁(T) coincide if we plot them versus T/H (see also experimental results of [#!mchenry!#]). The curves we measured clearly don't (see figure and ).

Figure: Two magnetization recovery curves in SrB₆, one at 1.07 T, the other at 4.75 T. They clearly do not coincide!

$\includegraphics[width=10cm]{eps_figures/SrB6;tworecoveries.eps}$

Further more it would be very surprising if we had that good coincidence of both CaB₆ and SrB₆. It would tell us that there are impurities systematically built in and one would have to expect them to be in other samples as well. But there has not been found anything.
A last argument against that objection is that none of the two functions fits properly to the data (see appendix ). The best fits we could obtain were with a g-factor of the order of 0.1 -- a physically very unlikely value (from the definition of the g-factor: $1 \le g \le 2$ ).
Summarized we may say that if there were impurities in our sample they may cause a certain contribution to the spin-lattice relaxation rate but they can't explain all the phenomenon.
However it should be mentioned that an attempt to give an upper limit of the impurity concentration from the susceptibility data failed. A plot of the susceptibility data is shown in figure . Fits to the Curie tail in data sets taken at various fields showed self-consistenly an impurity concentration of about 0.6% (we choosed the effective Bohr magneton number in the Curie law to be p=1). But since these data are taken in a bulk sample (powdered crystal) we can not distinguish between impurities in the crystalline structure and impurities on the surface. Because of the arguments given above we plead for impurities on the surface of the powder grains. Such impurities contribute significantly to the susceptibility but they don't show up in the NMR signal. A future measurement on a single non-powdered crystal would maybe help.

Summary

Next: Summary Up: Results Previous: The Spin-Spin Relaxation Rate



Effekte der Physik und ihre Anwendungen (Taschenbuch) von Manfred von Ardenne, Gerhard Musiol, Siegfried Reball

Siehe auch:

Grundkurs Theoretische Physik 2. Analytische Mechanik: v. 2 (Springer-Lehrbuch) von Wolfgang Nolting

Experimentalphysik, Bd. 3. Atome, Moleküle und Festkörper von Wolfgang Demtröder

Grundkurs Theoretische Physik 1. Klassische Mechanik von Wolfgang Nolting

Klassische Elektrodynamik von John D. Jackson

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